Techniques for controlling small angle Mølmer-Sørensen gates and for handling asymmetric spam errors

ABSTRACT

The disclosure describes various techniques to control of small angle Mølmer-Sørensen (MS) gates and to handle asymmetric errors. A technique is described for handling asymmetric errors in quantum information processing (QIP) systems. An exemplary method includes implementing a quantum circuit in the QIP system that has first and second qubit lines, with a first qubit state having a greater measurement error than a second qubit state; swapping the roles of the first and second qubit states at a quantum circuit level in response to at least one of the first qubit line and the second qubit line being expected to be at the first qubit state at a measurement; and enabling a quantum simulation using the quantum circuit with the first and second qubit states reassigned in at least one of the first qubit line and the second qubit line after the swapping of the respective roles.

CROSS REFERENCE TO RELATED APPLICATION

The present application is a divisional of U.S. patent application Ser.No. 16/708,207, filed Dec. 9, 2019, which claims priority to and thebenefit from U.S. Provisional Patent Application No. 62/797,014, filedon Jan. 25, 2019, both being entitled “TECHNIQUES FOR CONTROLLING SMALLANGLE MØLMER-SØRENSEN GATES AND FOR HANDLING ASYMMETRIC SPAM ERRORS,”and the contents of each of which are incorporated herein by referencein their entirety.

BACKGROUND OF THE DISCLOSURE

Aspects of the present disclosure generally relate to quantum circuitconstructions, and more specifically, to techniques for control of smallangle Mølmer-Sørensen (MS) gates and for handling asymmetricstate-preparation-and-measurement (SPAM) errors in quantum circuitoptimization.

Trapped atomic ions and superconducting circuits are two examples ofquantum information processing (QIP) approaches that have deliveredsmall yet already universal and fully programmable machines. In atrapped ion QIP, there exists a native two-qubit entangling protocol,such as MS gates. The ability to control the degree of entanglement ofthe MS gates under partially entangling conditions benefits quantumcircuit optimization for applications such as quantum chemistrycomputation, including those computations that use a variable quantumeigensolver (VQE) approach. This control requires careful calibrationbetween the degree of entanglement and the optical or radio frequency(RF) power used in connection with the MS gate. To date most calibrationschemes rely on the extrapolation from a full entanglement condition orother indirect measurements, which are time consuming and requireadditional efforts to handle the systematic errors of experimentalinstruments. A new method or technique that can be used to measure andcalibrate the degree of entanglement of MS gates without the drawbacksmentioned above is highly desirable.

Moreover, when the QIP system has SPAM errors between the two qubitstates, circuit implementation techniques that makes the computationresults less susceptible to such errors in the QIP system are alsodesirable. In some instances, such techniques may be used in connectionwith the measurement and calibration of the degree of entanglement of MSgates.

SUMMARY OF THE DISCLOSURE

The following presents a simplified summary of one or more aspects inorder to provide a basic understanding of such aspects. This summary isnot an extensive overview of all contemplated aspects, and is intendedto neither identify key or critical elements of all aspects nordelineate the scope of any or all aspects. Its purpose is to presentsome concepts of one or more aspects in a simplified form as a preludeto the more detailed description that is presented later.

In an aspect of the disclosure, a method for calibrating quantum gatesis described that includes implementing, in a QIP system, a two-qubitcalibration circuit, the calibration circuit including a firstMølmer-Sørensen (MS) gate, MS(θ) gate, and a second MS gate, MS(−θ)gate, where θ represents an amount of entanglement of the MS gates;running the calibration circuit in the QIP system for a range of valuesof θ; measuring observed parity signals resulting from running thecalibration circuit, the two-qubit calibration circuit being configuredsuch that each of the observed parity signals is a direct measurement ofa different value of θ; generating calibration information thatdescribes the relationship between the values of θ in the range andtheir corresponding calibration observable measurements; and providingthe calibration information to arbitrarily calibrate one or more MSgates in a quantum simulation.

In an aspect of the disclosure, another method for calibrating quantumgates is described that includes receiving calibration information thatdescribes a relationship between parity signals and respective values ofθ within a range for MS gates, where θ represents an amount ofentanglement of the MS gates; applying optical or RF power to an MScalibration circuit for a target value of θ; measuring a parity signalfrom running the MS calibration circuit to determine if thecorresponding value of θ in the calibration information is the targetvalue of θ; in response to the corresponding value of θ being the targetvalue of θ, completing the calibration and enabling the MS gate for usein a quantum simulation; and in response to the corresponding smallvalue of θ not being the target value of θ, adjusting the optical or RFpower being applied to the MS gates in the MS calibration circuit untilthe measured parity signal corresponds to the target value of θ forcompleting the calibration and enabling the MS gate for use in a quantumsimulation.

In another aspect of the disclosure, a QIP system for calibratingquantum gates is described that includes a calibration componentconfigured to control one or more components of the QIP system for:implementing a two-qubit calibration circuit, the calibration circuitincluding a first MS gate, MS(θ) gate, and a second MS gate, MS(−θ)gate, where θ represents an amount of entanglement of the MS gates;running the calibration circuit for a range of values of θ; measuringobserved parity signals resulting from running the calibration circuit,the two-qubit calibration circuit being configured such that each of theobserved parity signals is a direct measurement of a different value ofθ; and generating calibration information that describes therelationship between the values of θ in the range and theircorresponding calibration observable measurements. The QIP system mayalso include a memory for storing the calibration information, whereinthe calibration component is configured to access the calibrationinformation in the memory to provide the calibration information to theone or more components of the QIP system to arbitrarily calibrate one ormore MS gates in a quantum simulation. The one or more components of theQIP system may include one or more of a trap (e.g., an atom or ion trp),an optical controller, an algorithms component, or any of theirsub-components.

In another aspect of the disclosure, a QIP system for calibratingquantum gates is described that includes a memory storing calibrationinformation that describes a relationship between parity signals andrespective values of θ within a range for MS gates, where θ representsan amount of entanglement of the MS gates; and a calibration componentconfigured to control one or more components of the QIP system for:receiving the calibration information; applying optical or RF power toan MS calibration circuit for a target value of θ; measuring a paritysignal from running the MS calibration circuit to determine if thecorresponding value of θ in the calibration information is the targetvalue of θ; in response to the corresponding value of θ being the targetvalue of θ, completing the calibration and enabling the MS gate for usein a quantum simulation; and in response to the corresponding value of θnot being the target value of θ, adjusting the optical or RF power beingapplied to the MS gates in the MS calibration circuit until the measuredparity signal corresponds to the target value of θ for completing thecalibration and enabling the MS gate for use in a quantum simulation.The one or more components of the QIP system may include one or more ofa trap (e.g., an atom or ion trap), an optical controller, an algorithmscomponent, or any of their sub-components.

In another aspect of the disclosure, a method for handling asymmetricSPAM errors in QIP systems is described that includes implementing aquantum circuit in the QIP system, where the quantum circuit has atleast a first qubit line and a second qubit line, a first qubit state inthe QIP system has a greater measurement error than a second qubit statein the QIP system, swapping the role of the first qubit state and thesecond qubit state at a quantum circuit level in response to the firstqubit line and/or the second qubit line being expected to be at thefirst qubit state at measurement, and enabling a quantum simulationusing the quantum circuit with the first qubit state and the secondqubit state reassigned in the first qubit line and/or the second qubitline after the swapping of their roles.

In another aspect of the disclosure a QIP system for handling asymmetricSPAM errors is described that includes an asymmetric error componentconfigured to control one or more components of the QIP system for:implementing a quantum circuit in the QIP system, wherein the quantumcircuit has at least a first qubit line and a second qubit line, and afirst qubit state in the QIP system has a greater measurement error thana second qubit state in the QIP system; swapping the role of the firstqubit state and the second qubit state at a quantum circuit level inresponse to the first qubit line and/or the second qubit line beingexpected to be at the first qubit state at measurement; and performing aquantum simulation using the quantum circuit with the first qubit stateand the second qubit state reassigned in the first qubit line and/or thesecond qubit line after the swapping of their roles. The one or morecomponents of the QIP system may include one or more of a trap (e.g., anatom or ion trap), an optical controller, an algorithms component, orany of their sub-components.

Described herein are methods and systems for various aspects associatedwith techniques for control of small angle Mølmer-Sørensen (MS) gatesand for handling asymmetric SPAM errors. At least some aspects of thesemethods and systems may be implemented in a computer-readable storagemedium having computer-executable code that when executed performs thevarious functions of these methods and systems.

BRIEF DESCRIPTION OF THE DRAWINGS

The appended drawings illustrate only some implementation and aretherefore not to be considered limiting of scope.

FIG. 1 is a diagram that illustrates an example of a two-qubitcalibration circuit in accordance with aspects of this disclosure.

FIG. 2 is a diagram that illustrates an example of a calibration curvethat provides a relationship between a degree or amount of entanglement,θ, and parity signals in accordance with aspects of this disclosure.

FIG. 3 is a diagram that illustrates another example of a two-qubitcalibration circuit with a NOT gate in accordance with aspects of thisdisclosure.

FIG. 4A is a flow chart that illustrates a method to obtain calibrationinformation for small angle MS gates in accordance with aspects of thisdisclosure.

FIG. 4B is a flow chart that illustrates a method for calibrating smallangle MS gates in accordance with aspects of this disclosure.

FIG. 5 is a flow chart that illustrates a method for handling asymmetricerrors in accordance with aspects of this disclosure.

FIG. 6 is a block diagram of a computer device in accordance withaspects of this disclosure.

FIG. 7 is a block diagram that illustrates an example of a QIP system inaccordance with aspects of this disclosure.

DETAILED DESCRIPTION

The detailed description set forth below in connection with the appendeddrawings is intended as a description of various configurations and isnot intended to represent the only configurations in which the conceptsdescribed herein may be practiced. The detailed description includesspecific details for the purpose of providing a thorough understandingof various concepts. However, it will be apparent to those skilled inthe art that these concepts may be practiced without these specificdetails. In some instances, well known components are shown in blockdiagram form in order to avoid obscuring such concepts.

As described above, trapped atomic ions and superconducting circuits aretwo examples of QIP approaches that have delivered small yet alreadyuniversal and fully programmable machines. In trapped ion QIP,interactions may be naturally realized as extensions of common two-qubitgate interactions. Therefore, it is desirable to use entangling gatesfor efficient (e.g., reduced gate count) quantum circuit constructionsto implement interactions in trapped ion technology. One particularinteraction available in the use of trapped ions for quantum computingis the so-called Mølmer-Sørensen (MS) gate, also known as the XXcoupling or Ising gate. To achieve computational universality, theMølmer-Sørensen gate (either locally addressable or globallyaddressable) is complemented by arbitrary single-qubit operations.

In this disclosure, a two-qubit quantum circuit to calibrate the MSgates is proposed. The parity signal of a two-ion pair is measured asthe feature of the entanglement of the MS gate. This provides amodel-independent method to measure and calibrate MS gates at anarbitrary angle with the higher accuracy than the traditional methods.In addition this method can be integrated in a quantum system toactively control and to feedback the degree of entanglement.

Traditionally the calibration of small angle MS gates is implemented intwo ways. The first method is measuring the number of gates required toachieve the full entanglement. The second method relies on separateexperiments that calibrate the radio-frequency or optical power appliedto the qubit.

In the first traditional calibration method, it only applies to thesituations when the full entanglement angle, π/2, is a multiple of adegree of entanglement (θ) of interest. For any other angles, anextrapolation operation is required and the calibration becomes fitmodel-dependent. Moreover when the θ is small, many MS gates arerequired to reach full entanglement such that other incoherence andexperimental imperfections are likely to affect the quality of thecalibration.

In the second traditional calibration method, even though it can applyto arbitrary angles, it does not actually calibrate the degree ofentanglement directly but, instead, it calibrates other physicalquantities, and propagates the results to the operation of MS gates.Accordingly, the imperfections that occur in the propagation process arenot included in the measurement (calibration) process.

The techniques proposed in this disclosure may be used to measure andcalibrate any arbitrary angles with only two MS gates. Therefore it isless sensitive to other experimental shortcomings. Moreover since theentanglement quantity is measured directly, these techniques can beimplemented in a closed-loop feedback control system to actively servo(e.g., dynamically control) the degree of entanglement of one or more MSgates.

In a similar spirit to calibrating the system that enhances theperformance of the quantum computer, another consideration is theasymmetric error rates that occur when measuring |0

and |1

qubit states to improve the quality of the computational results.Consider, for instance, a case where a qubit line is expected to be inthe |1

qubit state at measurement and the |1

qubit state had greater measurement errors than the |0

qubit state. In this case, it may be best to redefine or reassign therepresentations or conditions of the |0

and |1

qubit states. This approach may end up modifying the circuit but thecomputation performed is equivalent and the measurement errors arereduced.

Additional details of both the calibration of MS gates and the handlingof asymmetric measurement errors are provided below.

As mentioned above, traditionally when thinking about quantum computinga set of universal gates are considered that include or involve somearbitrary single-qubit gates and also at least one two-qubit gate suchas a controlled-NOT gate. The controlled-NOT gate has two (2) inputqubits and one of them is flipped based on the state of the other. TheMølmer-Sørensen or MS gate is a similar gate having two input qubits,where if you input IOU) the output of the MS gate is (|00

+|11

)/√{square root over (2)} if the MS gate parameter is set to is fullyentangle the two qubits. Accordingly, the MS gate is typicallycharacterized for its fully entanglement setting.

It turns out, however, that when the power or intensity of the laser orlaser sources applied to the MS gate is reduced or turned down, insteadof the output of the MS gate being (|00

+|11

)/√{square root over (2)}, the output of the MS gate can be

$\left. {\left. {\cos\frac{\theta}{2}{❘00}} \right\rangle + {\sin\frac{\theta}{2}{❘11}}} \right\rangle,$which means that for small θ (e.g., a small amount or degree ofentanglement), the output of the MS gate can be approximately (|00

with a small fraction of |11

added in. These are clearly more complicated gates than the fullyentangling MS gate and may not be best for use as universal gates,however, these types of MS gates are very useful in certain types ofproblems, including in the simulation or solution of quantum chemistryproblems. The use of small-angle MS gates can also be very useful inquantum approximate optimization algorithms and quantum machine learningalgorithms, for example. Then the issue with these gates is how to tunethe power of lasers or RF sources correctly to get the right θ, that is,the right amount or degree of entanglement.

In the full entangled case, θ=π/2 such that

${\cos\frac{\theta}{2}} = {\sin\frac{\theta}{2}}$and the output of the MS gate is (|00

+|11

)/√{square root over (2)}. For small values of θ, the angles arearbitrary. For example, the angles can be instead θ=π/20 or θ=π/25, orany other small values. If the power of the optical beams or RF sourcesdrifts higher, then the angle becomes larger and the degree ofentanglement can change to an undesirable value. There needs to be anefficient and effective way to calibrate or control the laser power toget the right angle.

The calibration process can present some challenges. As described abovein connection with the first traditional method, if the target angle isθ=π/20, for example, one approach is to repeat this ten (10) times sothat θ=π/20 becomes θ=π/2=10×π/20 and get a fully entangled state. Oncethe fully entangled state is achieved there are standard approaches thatcan be taken to characterize how well has the fully entanglement beenachieved, for example, by looking at the population of parities of thequbit pair and estimate how well the entangled state was created. Anentanglement witness can be used to determine if there is entanglementand how well it was done (e.g., the fidelity of the operation). So thisapproach works when θ=π/2 is a multiple of the desired or target angle,but does not work so well when the target angle is θ=π/13 or θ=π/25, forexample, for which there is no multiple to get to θ=π/2. Moreover, asdescribed above, for any other angles for which θ=π/2 is not a multipleof the desired or target angle, extrapolation is required and thecalibration becomes fit model-dependent. When θ is small (e.g. has asmall value), many MS gates are required such that other incoherence andexperimental imperfection may affect the quality of the calibration.

As described above in connection with the second traditional method,another approach is to calibrate physical quantities other than theangle directly. For example, the amount of laser power on an MS gatethat is needed to obtain a particular or desirable θ may be determinedbased on how much radio frequency (RF) power is applied to acousto-opticmodulators (AOMs) in a QIP system that are used to control the power ofRF sources or optical beams (e.g., the AOMs may operate as laserswitches). In this approach, the envelope shape of the laser pulseapplied to the MS gate is amplitude modulated (e.g., modulate the laserpower) through the RF power/AOM to get a spin entanglement at the end ofthe MS gate and vary the amplitude of the laser pulse (e.g., vary thelaser power) to control the degree of entanglement or the entangledstate being created.

Therefore, if it is determined that a certain amount of RF power (andtherefore a corresponding amount of laser power) is needed to get fullentanglement (θ=π/2), then the amount of RF power reduction that isneeded for a smaller angle MS gate is proportional to squared root ofthe relative difference between the small angle and π/2. For example, if2 Watts of power are needed for full entanglement (θ=π/2), then to getan angle that is ten (10) times smaller (θ=π/20), the amount of powerneeded has to be scaled down by a factor of √{square root over (10)}, sothat approximately 0.6 Watts are needed for θ=π/20. It turns out,however, that AOMs and/or other laboratory instruments may havenon-linear responses and such a direct scaling of physical quantities(e.g., RF and/or optical power) does not work as well as needed.Moreover, as described above, this approach does not actually calibratethe degree of entanglement directly but, instead, it calibrates otherphysical quantities, and propagates the results to the operation of MSgates where the imperfections happening in the propagation process isnot included in the calibration process. Trying to characterize thesmall angle MS and calibrate the laser power can be a challengingproblem.

In order to have a better measurement and calibration approach ofarbitrary angle MS gates, a technique based on only two MS gates isproposed.

FIG. 1 is a diagram 100 that illustrates an example of a two-qubitcalibration circuit in accordance with aspects of this disclosure. Thequantum circuit in the diagram 100, also referred to as a quantumcalibration circuit or simply a calibration circuit, consists of onlytwo small angle MS gates to measure and calibrate the degree ofentanglement of an MS gate, θ. The quantum circuit includes an S gate120 a, a first MS gate 110 a, MS(θ), two S^(†) gates 120 b and 120 c, asecond MS gate 110 b, MS(−θ), an S gate 120 d, two Hadamard (H) gates130 a and 130 b, and two measurements 140 a and 140 b. The quantumcircuit has a top or first qubit line 150 a and a bottom or second qubitline 150 b.

The state of the two-qubit system of the quantum circuit in the diagram100 can be represented as a 4×1 vector

$\begin{bmatrix}C_{00} \\C_{01} \\C_{10} \\C_{11}\end{bmatrix}$the components of which represent the amplitude of quantum statesψ=C₀₀|00

+C₀₁|01

+C₁₀|10

+C₁₁|11

. The amplitude is a complex number, and the experimentally observedvalue is the absolute square (AS) of the complex amplitude. Accordingly,the application of quantum circuits can be modeled as the matrixmultiplication. All the gates shown in the quantum circuit in thediagram 100 can be represented as:

${H = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}}},$ ${S = \begin{bmatrix}1 & 0 \\0 & i\end{bmatrix}},{and}$ ${{MS}(\theta)} = {\begin{bmatrix}{\cos{\theta/2}} & 0 & 0 & {{- i}\sin{\theta/2}} \\0 & {\cos{\theta/2}} & {{- i}\sin{\theta/2}} & 0 \\0 & {{- i}\sin{\theta/2}} & {\cos{\theta/2}} & 0 \\{{- i}\sin{\theta/2}} & 0 & 0 & {\cos{\theta/2}}\end{bmatrix}.}$

As described above, the angle θ represents the amount of theentanglement created after the MS interaction (θ=π/2 corresponds to thefull entanglement). Hence the matrix representation of the fulltwo-qubit calibration circuit is

${\frac{1}{2}\begin{bmatrix}\left( {{\cos\theta} - {\sin\theta}} \right) & 1 & 1 & \left( {{\cos\theta} + {\sin\theta}} \right) \\\left( {{\cos\theta} + {\sin\theta}} \right) & {- 1} & 1 & \left( {{{- \cos}\theta} + {\sin\theta}} \right) \\\left( {{\cos\theta} + {\sin\theta}} \right) & 1 & {- 1} & \left( {{{- \cos}\theta} + {\sin\theta}} \right) \\\left( {{\cos\theta} - {\sin\theta}} \right) & {- 1} & {- 1} & \left( {{\cos\theta} + {\sin\theta}} \right)\end{bmatrix}}.$

Note that there may be many different matrix representations of thequantum circuit presented here, and what is being shown represents oneconvention. Before the experiment, the two-qubit state is initialized to|00

, or

$\begin{bmatrix}1 \\0 \\0 \\0\end{bmatrix}$in the matrix notation being used in this convention. The expectedprobability amplitude output of the circuit is

${\frac{1}{2}\begin{bmatrix}\left( {{\cos\theta} - {\sin\theta}} \right) \\\left( {{\cos\theta} + {\sin\theta}} \right) \\\left( {{\cos\theta} + {\sin\theta}} \right) \\\left( {{\cos\theta} - {\sin\theta}} \right)\end{bmatrix}}.$Therefore, the observed parity signal, defined as

${{AS}\left( \frac{{\cos\theta} - {\sin\theta}}{2} \right)} + {A{S\left( \frac{{\cos\theta} - {\sin\theta}}{2} \right)}} - {A{S\left( \frac{{\cos\theta} + {\sin\theta}}{2} \right)}} - {A{S\left( \frac{{\cos\theta} + {\sin\theta}}{2} \right)}}$and is given by P=−sin(2·θ). Therefore, the two-qubit calibrationcircuit may be used to directly measure the angle of the MS gate. Thisbenefits accurate implementation of quantum circuits that require aprecise control of the entanglement.

FIG. 2 shows a diagram 200 that illustrates an example of a calibrationcurve that provides a relationship between a degree or amount ofentanglement, θ, and parity signals in accordance with aspects of thisdisclosure. For example, the calibration curve shows the relationshipbetween the expected parity signal and the degree or amount ofentanglement, θ. This calibration curve, which results from using thetwo-qubit calibration circuit described above and measuring thecorrelation at the output, can be stored and used to calibrate differentMS gates of arbitrary angles.

The approach described in connection with FIGS. 1 and 2 provides a morepractical way to calibrate the laser power (or the RF power used tocontrol the laser power) so that it is possible to tune the MS gates tothe desired degree or amount of entanglement, θ. In this approach, θ isthe parameter of the MS gate that can be controlled, and the parity isthe population of the qubits that can be measured very accurately. Oneway to use the calibration information in the calibration curvegenerated by running the two-qubit calibration circuit is to first tunethe laser power for the MS gate, measure the parity that results fromthe MS gate and infer the angle θ from the calibration curve. The laserpower may be adjusted or tuned until the parity measurements give thedesired or target angle θ.

In a similar spirit to calibrating the MS gates to enhance theperformance of the quantum computations or quantum simulations beingperformed, another consideration may be to take account for the existingof asymmetric error rates in measuring qubit states |10

and |1

, and ways to improve the quality of the computational results in viewof this difference. Consider, for instance, a case where a qubit line isexpected to be in the |1

state at measurement but the measurement error of the |1

qubit state is greater than the measurement error of the |0

qubit state. In this case, it may be better to redefine or reassign thequbit state of the qubit so that the new |0

qubit state represents the old |0

qubit state and vice versa. This approach may modify the quantum circuitbut the computation performed is equivalent.

That is, there may be two qubit states, |0

and |1

, and the qubit state |0

has a smaller measurement error so it may be desirable that the output(e.g., at measurement) be |0

as much as possible to reduce the computational error. In a case, asdescribed above, where the output at measurement would have been thequbit state |1

instead, one modification that can be made to the quantum circuit is toapply a NOT gate to the front of the qubit line where the qubit state |1

would appear at the output, then propagate the NOT gate to the end ofthe qubit line to make the output a qubit state |1

to avoid the higher measurement error of the qubit state |1

, and do the |0

to |1

qubit flip as part of the process.

One example where such a technique may be applied is in quantumchemistry simulations. For example, there may be a simulation (e.g., asimulation using a quantum circuit) where there are two qubits, oneassociated with a top or first qubit line of a quantum circuit andanother associated with a bottom or second qubit line of the quantumcircuit. The top qubit may represent a top orbital (e.g., an electronorbital in an atom or molecule) and the bottom qubit may represent abottom orbital. An electron can be either in the top orbital or thebottom orbital. One simple representation of such as system may have thequbit state |1

represent the electron being in the orbital and the qubit state |0

represent the electron not being in the orbital.

Such a two-qubit quantum chemistry circuit may be initially prepared tohave |0

in the top qubit line and |0

in the bottom qubit line. To represent that there is an electron on thetop qubit line, the qubit state in the top qubit line is changed to a |1

. Accordingly, the system is initialized to say that the electron is inthe top orbital (i.e., the top qubit line) and not in the bottom orbital(i.e., the bottom qubit line). The quantum chemistry circuit can be runand measurements can be made. However, the QIP system on which thequantum chemistry circuit is run can have asymmetric state preparationand measurement (SPAM) errors such that qubit states |0

have small errors and qubit states |1

have large errors (the opposite may also be the case).

Because the qubit state |1

can be on the top qubit line for the most part throughout the entiresimulation, it will likely incur larger measurement errors. To avoidthis issue, the proposed technique involves changing the representation(e.g., reassign) of having an electron in the top orbital to be thequbit state |0

instead since such a representation is arbitrary anyway. Now, for thetop qubit line, having an electron in the top orbital is represented bythe qubit state |0

and not having an electron in the top orbital is represented by thequbit state |1

). For the bottom qubit line the representation remains as before, withhaving an electron in the bottom orbital being represented by the qubitstate |1

and not having an electron in the bottom orbital being represented bythe qubit state |0

. The quantum chemistry circuit can be run and measurements made. If thetop qubit line/top orbital results in a |0

then the electron is there, and if results in a |1

then the electron is not there. For the bottom qubit line/bottomorbital, if a |0

results then the electron is not there, and if a |1

results then the electron is there. These results can be interpreted inthe opposite way classically.

The technique described above may apply to different types of quantumcircuits and not just quantum chemistry circuits used in quantumchemistry simulations. By changing the designation or representation ofconditions to the qubit states it is possible to reduce SPAM errorsassociated with those qubit states that are more susceptible to errorsand reduce the error of the entire quantum circuit. This technique maybe applicable to calibration circuits such as the two-qubit calibrationcircuit described in connection with the diagram 100 in FIG. 1 .

For example, FIG. 3 illustrates a diagram 300 in which a similar circuitto the two-qubit calibration circuit from FIG. 1 is augmented with a NOTgate 310 on, say, the beginning of the top qubit line 150 a. Moreover,gates 120 a and 120 b are replaced by gates 320 a and 320 brespectively, and the gates H 130 a and H 130 b are optional (dottedlines) and kept if the circuit is used as an MS calibration circuit. Toapply the technique described above of redefining or reassigning thequbit states for handling cases where there are asymmetric SPAM errorsin the system, the NOT gate 310 may be propagated through the top qubitline 150 a to the end of the top qubit line 150 a before the measurement140 a. This may be accomplished by employing certain rules, some ofwhich are described below:

-   -   (1) a NOT gate followed by an Rz(Ø) gate is equivalent to an        Rz(−Ø) gate followed by the NOT gate (NOT-Rz(Ø)=Rz(−Ø)-NOT),        where the Rz(Ø) gate is a single-qubit Z-rotation by angle Ø,    -   (2) a NOT gate followed by an MS gate, MS(θ) gate, is equivalent        to an MS(θ) gate followed by the NOT gate (NOT-MS(θ)=MS(θ)-NOT),        where MS(θ) gate is a continuous-parameter MS gate, and    -   (3) a NOT gate followed by a Hadamard gate, H gate, is        equivalent to an H gate followed by a Z gate (NOT-H=H−Z), where        a Z gate is described as

$Z = {\begin{bmatrix}1 & 0 \\0 & {- 1}\end{bmatrix}.}$

With these rules, it is possible to propagate the initial NOT gate tothe end of the circuit. Doing so reduces the error in the computationdue to the measurement, since the qubit is now expected to be mostly inthe lower error qubit state (e.g., in the qubit state |0

when that is the state that produces the smallest errors).

There are two different cases to consider once the NOT gate ispropagated to the end of the quantum circuit, either the qubit line endswith a NOT gate or with a Z gate (see e.g., rule (3) above). For thissituation, the following additional rules may be used:

-   -   (1) a NOT gate followed by a measurement at the end of the        quantum circuit is equivalent to a measurement followed by a        “classical flip,” and    -   (2) a Z gate followed by a measurement at the end of the quantum        circuit is equivalent to a measurement.        In this instance, a “classical flip” means that, if we measure        |0        , we interpret it as |1        and vice versa. The Z gate followed by a measurement is no        different from the measurement since adding a −1 phase to a |1        state does not alter the measurement probability.

As mentioned above, the technique described herein for handlingasymmetric errors in measurement may be applied to any quantum circuit,that is, this technique may be hardware agnostic. This is because, inprinciple, it is generally possible to come up with appropriatecommutation rules for any native gateset applicable for any hardware.This means that, whenever it is the case that we know that a qubit lineis expected to be mostly in the higher measurement error state (e.g.,the qubit state |1

in the examples provided above), the quantum computer fidelity may beimproved by redefining or reassigning the representation of the qubitstates.

FIG. 4A is a flow chart that illustrates a method 400 a to obtaincalibration information for small angle MS gates in accordance withaspects of this disclosure. In an aspect, the method 400 a may beperformed in a computer system such as a computer system 600 describedbelow in connection with FIG. 6 , where, for example, the processor 610,the memory 620, the data store 640, and/or the operating system 660 maybe used to perform the functions of the method 400 a. In another aspect,the method 400 a may be performed by a QIP system such as the QIP system705 described below in connection with FIG. 7 , where, for example, acalibration component 780 and/or a calibration table 785 may be used toperform the functions of the method 400 a.

At 410, the method 400 a may include implementing, in a QIP system, atwo-qubit calibration circuit, the calibration circuit including a firstMS gate, MS(θ) gate, and a second MS gate, MS(−θ) gate, where θrepresents an amount of entanglement of the MS gates.

At 415, the method 400 a may include running the calibration circuit inthe QIP system for a range of values of θ.

At 420, the method 400 a may include measuring observed parity signalsresulting from running the calibration circuit, the two-qubitcalibration circuit being configured such that each of the observedparity signals is a direct measurement of a different value of θ.

At 425, the method 400 a may include generating calibration informationthat describes the relationship between the values of θ in the range andtheir corresponding calibration observable measurements.

At 430, the method 400 a may include providing the calibrationinformation to arbitrarily calibrate one or more MS gates in a quantumsimulation.

In an aspect of the method 400 a, the method may further includeinitializing the two-qubit calibration circuit to |00

.

In another aspect of the method 400 a, θ=π/2 may represent fullentanglement and the values of θ are those for which |θ|<<π/2.

In another aspect of the method 400 a, the range of values of θ includesvalues of θ between θ=−0.5 π and θ=0.5π (in radians).

In another aspect of the method 400 a, the range of values of θ includesarbitrary values of θ within that range.

In another aspect of the method 400 a, the two-qubit calibration circuitis configured to produce an expected output of

$\frac{1}{2}\begin{bmatrix}\left( {{\cos\theta} - {\sin\theta}} \right) \\\left( {{\cos\theta} + {\sin\theta}} \right) \\\left( {{\cos\theta} + {\sin\theta}} \right) \\\left( {{\cos\theta} - {\sin\theta}} \right)\end{bmatrix}$such that the observed parity signal P=−sin(2·θ) for a particular θ isobtained from the expected probability amplitude output.

In another aspect of the method 400 a, the two-qubit calibration circuithas a top qubit line and a bottom qubit line, the method 400 a furtherincluding applying a NOT operation to the top qubit line such that theobserved parity signal P=sin(2·θ) for a particular θ is obtained fromthe expected output.

In another aspect of the method 400 a, implementing the two-qubitcalibration circuit having the first MS gate and the second MS gateincludes implementing the two-qubit calibration circuit described in thediagram 100 in FIG. 1 .

In another aspect of the method 400 a, running the calibration circuitfor a range of small values of θ includes varying optical or RF powerapplied to the two-qubit calibration circuit to produce the observedparity signals.

In another aspect of the method 400 a, implementing the two-qubitcalibration circuit in the QIP system includes implementing thetwo-qubit calibration circuit using atoms or ions in a trap of the QIPsystem (see e.g., ion trap 770 in QIP system 705).

In another aspect of the method 400 a, the values of θ includes smallvalues of θ.

In yet another aspect of the method 400 a, generating the calibrationinformation includes generating a table with the calibrationinformation, and providing the calibration information includesproviding the table.

As described above, the method 400 a may be performed in connection witha QIP system configured for calibrating quantum gates, where such QIPsystem may include a calibration component configured to control one ormore components of the QIP system for implementing a two-qubitcalibration circuit, the calibration circuit including a first MS gate,MS(θ) gate, and a second MS gate, MS(−θ) gate, where θ represents anamount of entanglement of the MS gates; for running the calibrationcircuit for a range of values of θ; for measuring observed paritysignals resulting from running the calibration circuit, the two-qubitcalibration circuit being configured such that each of the observedparity signals is a direct measurement of a different value of θ; andfor generating calibration information that describes the relationshipbetween the values of θ in the range and their corresponding calibrationobservable measurements. The QIP system may further include a memory(e.g., in the calibration component or separate from the calibrationcomponent) for storing the calibration information, wherein thecalibration component is configured to access the calibrationinformation in the memory to provide the calibration information to theone or more components of the QIP system to arbitrarily calibrate one ormore MS gates in a quantum simulation. The one or more components of theQIP system may include one or more of a trap, an optical controller, analgorithms component, or any of their sub-components (see e.g., QIPsystem 705).

FIG. 4B is a flow chart that illustrates a method 400 b for calibratingsmall angle MS gates in accordance with aspects of this disclosure. Inan aspect, the method 400 b may be performed in a computer system suchas a computer system 600 described below in connection with FIG. 6 ,where, for example, the processor 610, the memory 620, the data store640, and/or the operating system 660 may be used to perform thefunctions of the method 400 b. In another aspect, the method 400 b maybe performed by a QIP system such as the QIP system 705 described belowin connection with FIG. 7 , where, for example, an calibration component780 and/or a calibration table 785 may be used to perform the functionsof the method 400 b.

At 450, the method 400 b may include receiving calibration informationthat describes a relationship between parity signals and respectivesmall values of θ within a range for MS gates, where θ represents anamount of entanglement of the MS gates.

At 455, the method 400 b may include applying an optical beam to an MScalibration circuit (e.g., the two-qubit calibration circuit in thediagram 100 in FIG. 1 ) for a target value of θ.

At 460, the method 400 b may include measuring a parity signal fromrunning the MS calibration circuit to determine if the correspondingvalue θ in the calibration information is the target value of θ.

At 465, the method 400 b may include in response to the correspondingvalue of θ being the target value of θ, completing the calibration andenabling the MS gate for use in a quantum simulation.

At 470, the method 400 b may include in response to the correspondingvalue of θ not being the target value of θ, adjusting optical or RFpower being applied to the MS gates in the MS calibration circuit untilthe measured parity signal corresponds to the target value of θ forcompleting the calibration and enabling the MS gate for use in a quantumsimulation.

In an aspect of the method 400 b, the method 400 b may further includeperforming the quantum simulation using the calibrated MS gate. Thequantum simulation may be a quantum chemistry simulation. The quantumsimulation may be a quantum approximate optimization algorithm or aquantum machine learning algorithm

In another aspect of the method 400 b, the method 400 b may furtherinclude detecting a deviation of the optical or RF power from theoptimal value used to apply the MS gate, and adjusting the optical or RFpower used to apply the MS gate until the measured parity signal fromthe MS calibration circuit again corresponds to the target small valueof θ for recalibrating the MS gate. The detecting and the adjusting maybe part of a closed-loop feedback control system to actively servo theamount of entanglement of the MS gate.

In another aspect of the method 400 b, θ=π/2 may represent fullentanglement and the values of θ are those for which |θ|<<π/2.

In another aspect of the method 400 b, the range of values of θ includesvalues of θ between θ=−0.5 π and θ=0.5π (in radians).

In another aspect of the method 400 b, the range of values of θ includesarbitrary values of θ within that range.

In another aspect of the method 400 b, the method 400 b may furtherinclude applying optical or RF power to run the MS calibration circuitfor a different target value of θ; measuring a parity signal fromrunning the MS calibration circuit to determine if the correspondingvalue of θ, in the calibration information is the different target valueof θ; in response to the corresponding value of θ being the differenttarget value of θ, completing the calibration and enabling of adifferent MS gate for use in the same quantum simulation as the MS gate;and in response to the corresponding value of θ not being the differenttarget value of θ, adjusting the optical or RF power being applied tothe MS gates in the MS calibration circuit until the measured paritysignal corresponds to the different target value of θ for completing thecalibration and enabling the of the different MS gate for use in thesame quantum simulation as the MS gate.

In another aspect of the method 400 b, the values of θ includes smallvalues of θ.

As described above, the method 400 b may be performed in connection witha QIP system configured for calibrating quantum gates, where such QIPsystem may include a memory storing calibration information thatdescribes a relationship between parity signals and respective smallvalues of θ within a range for MS gates, where θ represents an amount ofentanglement of the MS gates. The QIP system may further include acalibration component configured to control one or more components ofthe QIP system for receiving the calibration information; for applyingoptical or RF power to run an MS calibration circuit for a target valueof θ; for measuring a parity signal from running the MS calibrationcircuit to determine if the corresponding value of θ in the calibrationinformation is the target value of θ; in response to the correspondingvalue of θ being the target value of θ, for completing the calibrationand enabling the MS gate for use in a quantum simulation; and inresponse to the corresponding value of θ not being the target value ofθ, for adjusting the optical or RF power being applied to the MS gatesin the MS calibration circuit until the measured parity signalcorresponds to the target value of θ for completing the calibration andenabling the MS gate for use in a quantum simulation. The memory may bein the calibration component or separate from the calibration component.The one or more components of the QIP system may include one or more ofa trap, an optical controller, an algorithms component, or any of theirsub-components (see e.g., QIP system 705).

FIG. 5 is a flow chart that illustrates a method 500 for handlingasymmetric errors in accordance with aspects of this disclosure. In anaspect, the method 500 may be performed in a computer system such as acomputer system 600 described below in connection with FIG. 6 , where,for example, the processor 610, the memory 620, the data store 640,and/or the operating system 660 may be used to perform the functions ofthe method 500. In another aspect, the method 500 may be performed by aQIP system such as the QIP system 705 described below in connection withFIG. 7 , where, for example, an asymmetric error component 790 may beused to perform the functions of the method 500.

At 510, the method 500 may include implementing a quantum circuit in theQIP system, where the quantum circuit has at least a first qubit lineand a second qubit line, a first qubit state in the QIP system has agreater measurement error than a second qubit state in the QIP system.

At 515, the method 500 may include swapping the role of the first qubitstate and the second qubit state at a quantum circuit level in responseto the first qubit line and/or the second qubit line being expected tobe at the first qubit state at measurement.

At 520, the method 500 may include enabling a quantum simulation usingthe quantum circuit with the first qubit state and the second qubitstate reassigned in the first qubit line and/or the second qubit lineafter the swapping of their roles.

In an aspect of the method 500, the quantum circuit is part of a quantumchemistry circuit and the quantum simulation is a quantum chemistrysimulation. The method 500 further includes performing the quantumchemistry simulation using the quantum chemistry circuit with thereassigned first qubit state and second qubit state for the qubitline(s). Prior to the reassignment, the first qubit state indicates thatan electron is in an orbital and the second qubit states indicates thatthere is no electron in an orbital, where the first qubit linecorresponds to a top orbital and the second qubit line corresponds to abottom orbital. After the reassignment, the first qubit state indicatesthat there is no electron in an orbital and the second qubit stateindicates that there is an electron in an orbital.

In another aspect of the method 500, implementing the quantum circuitincludes applying a NOT gate to a start of the first qubit line toimplement the aforementioned reassignment of the first qubit state forthe first qubit line. Equivalently, the NOT gate can be appropriatelypropagated from the start of the first qubit line to an end of the firstqubit line. Propagating the NOT gate to the end of the first qubit lineis performed based on one or more rules in connection with one or moregates in the quantum circuit, the one or more rules including: the NOTgate followed by an Rz(θ) gate is equivalent to an Rz(−θ) gate followedby the NOT gate (NOT-Rz(θ)=Rz(−θ)-NOT), the NOT gate followed by an MSgate, MS(θ) gate, is equivalent to an MS(θ) gate followed by the NOTgate (NOT-MS(θ)=MS(θ)-NOT), where MS(θ) gate is a continuous-parameterMS gate, or the NOT gate followed by a Hadamard gate, H gate, isequivalent to an H gate followed by a Z gate (NOT-H=H−Z). Moreover,propagating the NOT gate to the end of the first qubit line based on theone or more rules results in either a NOT gate or a Z gate at the end ofthe first qubit line, the method further comprising: in response to thefirst qubit line ending in the NOT gate and then a measurement beingmade, performing the measurement and a classical flip, or in response tothe first qubit line ending in the Z gate and then a measurement beingmade, performing the measurement.

In another aspect of the method 500, implementing the quantum circuit inthe QIP system includes implementing the quantum circuit using atoms orions in a trap of the QIP system (see e.g., ion trap 770 in the QIP705).

In yet another aspect of the method 500, the quantum circuit is acalibration circuit for calibrating MS gates, and the calibrationcircuit includes a first MS gate, MS(θ) gate, and a second MS gate,MS(−θ) gate, where θ represents an amount of entanglement of the MSgates.

As described above, the method 500 may be performed in connection with aQIP system configured for handling asymmetric errors, where such QIPsystem may include an asymmetric error component configured to controlone or more components of the QIP system for implementing a quantumcircuit in the QIP system, where the quantum circuit has at least afirst qubit line and a second qubit line, and a first qubit state in theQIP system has a greater measurement error than a second qubit state inthe QIP system. The asymmetric error component may also be configuredfor swapping the role of the first qubit state and the second qubitstate at a quantum circuit level in response to the first qubit lineand/or the second qubit line being expected to be at the first qubitstate at measurement. The asymmetric error component may also beconfigured for enabling a quantum simulation using the quantum circuitwith the first qubit state and the second qubit state reassigned in thefirst qubit line and/or the second qubit line after the swapping oftheir roles. The one or more components of the QIP system may includeone or more of a trap, an optical controller, an algorithms component,or any of their sub-components (see e.g., QIP system 705).

Referring now to FIG. 6 , illustrated is an example computer device 600in accordance with aspects of the disclosure. The computer device 600can represent a single computing device, multiple computing devices, ora distributed computing system, for example. The computer device 600 maybe configured as a quantum computer, a classical computer, or acombination of quantum and classical computing functions. For example,the computer device 600 may be used for the calibration andimplementation of MS gates, and/or for handling asymmetric errormeasurements. Moreover, the computer device 600 may be used as a quantumcomputer and may implement quantum algorithms based on the techniquesdescribed herein.

In one example, the computer device 600 may include a processor 610 forcarrying out processing functions or methods associated with one or moreof the features described herein. The processor 610 may include a singleor multiple set of processors or multi-core processors. Moreover, theprocessor 610 may be implemented as an integrated processing systemand/or a distributed processing system. The processor 610 may include acentral processing unit (CPU), a quantum processing unit (QPU), agraphics processing unit (GPU), or combination of those types ofprocessors.

In an example, the computer device 600 may include a memory 620 forstoring instructions executable by the processor 610 for carrying outthe functions or methods described herein. In an implementation, forexample, the memory 620 may correspond to a computer-readable storagemedium that stores code or instructions to perform one or more of thefunctions, method, or operations described herein. In one example, thememory 620 may include instructions to perform aspects of the methods400 a, 400 b, and/or 500.

Further, the computer device 600 may include a communications component630 that provides for establishing and maintaining communications withone or more parties utilizing hardware, software, and services asdescribed herein. The communications component 630 may carrycommunications between components on the computer device 600, as well asbetween the computer device 600 and external devices, such as deviceslocated across a communications network and/or devices serially orlocally connected to computer device 600. For example, thecommunications component 630 may include one or more buses, and mayfurther include transmit chain components and receive chain componentsassociated with a transmitter and receiver, respectively, operable forinterfacing with external devices.

Additionally, the computer device 600 may include a data store 640,which can be any suitable combination of hardware and/or software, thatprovides for mass storage of information, databases, and programsemployed in connection with implementations described herein. Forexample, the data store 640 may be a data repository for operatingsystem 660 (e.g., classical OS, or quantum OS). In one implementation,the data store 640 may include the memory 620.

The computer device 600 may also include a user interface component 650operable to receive inputs from a user of the computer device 600 andfurther operable to generate outputs for presentation to the user or toprovide to a different system (directly or indirectly). The userinterface component 650 may include one or more input devices, includingbut not limited to a keyboard, a number pad, a mouse, a touch-sensitivedisplay, a digitizer, a navigation key, a function key, a microphone, avoice recognition component, any other mechanism capable of receiving aninput from a user, or any combination thereof. Further, the userinterface component 650 may include one or more output devices,including but not limited to a display, a speaker, a haptic feedbackmechanism, a printer, any other mechanism capable of presenting anoutput to a user, or any combination thereof.

In an implementation, the user interface component 650 may transmitand/or receive messages corresponding to the operation of the operatingsystem 660. In addition, the processor 610 may execute the operatingsystem 660 and/or applications or programs (e.g., programs to calibrateMS gates and/or for handling asymmetric error measurements), and thememory 620 or the data store 640 may store them.

When the computer device 600 is implemented as part of a cloud-basedinfrastructure solution, the user interface component 650 may be used toallow a user of the cloud-based infrastructure solution to remotelyinteract with the computer device 600.

FIG. 7 is a block diagram that illustrates an example of a QIP system705 in accordance with aspects of this disclosure. The QIP system 705may also be referred to as a quantum computing system, a computerdevice, or the like. In an aspect, the QIP system 705 may correspond toportions of a quantum computer implementation of the computer device 600in FIG. 6 .

The QIP system 705 may include a source 760 that provides atomic speciesto a chamber 750 having an ion trap 770 that traps the atomic speciesonce ionized by an optical controller 720. Optical sources 730 in theoptical controller 720 may include one or more light or optical beamsources that provide laser or optical beams that can be used forionization of the atomic species, control (e.g., phase control) of theatomic ions, for fluorescence of the atomic ions that can be monitoredand tracked by image processing algorithms operating in an imagingsystem 740 in the optical controller 720, and/or for implementing andcontrolling one or more gates, including MS gates and their degree ofentanglement. The imaging system 740 can include a high resolutionimager (e.g., CCD camera) for monitoring the atomic ions while they arebeing provided to the ion trap 770 (e.g., for counting) or after theyhave been provided to the ion trap 770 (e.g., for monitoring the atomicions states). In an aspect, the imaging system 740 may be implementedseparate from the optical controller 720, however, the use offluorescence to detect, identify, and label atomic ions using imageprocessing algorithms may need to be coordinated with the opticalcontroller 720.

The QIP system 705 may also include an algorithms component 710 that mayoperate with other parts of the QIP system 705 to perform quantumalgorithms associated with the features described above. As such, thealgorithms component 710 may provide instructions to various componentsof the QIP system 705 (e.g., to the optical controller 720) to enablethe implementation of quantum circuits, or their equivalents, such asthe ones described herein.

The QIP system 705 may also include the calibration component 780 andthe calibration table 785, which may be used in connection with otherparts of the QIP system 705 to perform the various features describedabove in connection with calibrating MS gates and using the calibratedMS gates in quantum circuits. Moreover, the QIP system 705 may furtherinclude the asymmetric error component 790, which may be used inconnection with other parts of the QIP system 705 to implement thetechniques described above for handling asymmetric measurement errors inthe system.

Although the present disclosure has been provided in accordance with theimplementations shown, one of ordinary skill in the art will readilyrecognize that there could be variations to the embodiments and thosevariations would be within the scope of the present disclosure.Accordingly, many modifications may be made by one of ordinary skill inthe art without departing from the scope of the appended claims.

What is claimed is:
 1. A method for handling asymmetric errors inquantum information processing (QIP) systems, the method comprising:implementing a quantum circuit in the QIP system, the quantum circuithaving at least a first qubit line and a second qubit line, wherein afirst qubit state in the QIP system has a greater measurement error thana second qubit state in the QIP system; swapping a first representationof the first qubit state and a second representation of the second qubitstate at a quantum circuit level in response to at least one of thefirst qubit line and the second qubit line being expected to be at thefirst qubit state at a measurement; and enabling a quantum simulationusing the quantum circuit with the first qubit state and the secondqubit state reassigned in at least one of the first qubit line and thesecond qubit line after the swapping of the respective representations.2. The method of claim 1, wherein the quantum circuit is part of aquantum chemistry circuit and the quantum simulation is a quantumchemistry simulation, and wherein the method further comprisesperforming the quantum chemistry simulation using the quantum chemistrycircuit with the reassigned first qubit state and second qubit state forthe first qubit line and/or the second qubit line.
 3. The method ofclaim 2, wherein, prior to the reassigning of the first qubit state andthe second qubit state, the first qubit state indicates that an electronis in an orbital and the second qubit state indicates that there is noelectron in an orbital, and wherein the first qubit line corresponds toa top orbital and the second qubit line corresponds to a bottom orbital.4. The method of claim 3, wherein, after the reassigning of the firstqubit state and the second qubit state, the first qubit state indicatesthat there is no electron in an orbital and the second qubit stateindicates that there is an electron in an orbital.
 5. The method ofclaim 1, wherein the implementing of the quantum circuit includesapplying a NOT gate to a start of the first qubit line to implement thereassigning of the first qubit state and the second qubit state orapplying the representations of the first qubit state and the secondqubit state in the quantum circuit.
 6. The method of claim 5, whereinthe applying of the NOT gate comprises propagating the NOT gate from thestart of the first qubit line to an end of the first qubit line topreserve an equivalence.
 7. The method of claim 5, wherein propagatingthe NOT gate to the end of the first qubit line is performed based oneor more rules in connection with one or more gates in the quantumcircuit, the one or more rules including: the NOT gate followed by anRz(Ø) gate is equivalent to an Rz(−Ø) gate followed by the NOT gate(NOT-Rz(Ø)=Rz(−Ø)-NOT), the NOT gate followed by a Mølmer-Sørensen (MS)gate, MS(θ) gate, is equivalent to an MS(θ) gate followed by the NOTgate (NOT-MS(θ)=MS(θ)-NOT), where MS(θ) gate is a continuous-parameterMS gate and θ is a degree or amount of entanglement of the MS gate, orthe NOT gate followed by a Hadamard gate, H gate, is equivalent to an Hgate followed by a Z gate (NOT-H=H−Z).
 8. The method of claim 7, whereinpropagating the NOT gate to the end of the first qubit line based on theone or more rules results in either a NOT gate or a Z gate at the end ofthe first qubit line, the method further comprising: in response to thefirst qubit line ending in the NOT gate and then a measurement beingmade, performing the measurement and a classical flip, or in response tothe first qubit line ending in the Z gate and then a measurement beingmade, performing the measurement.
 9. The method of claim 1, whereinimplementing the quantum circuit in the QIP system includes implementingthe quantum circuit using atoms or ions in a trap of the QIP system. 10.The method of claim 1, wherein: the quantum circuit is a calibrationcircuit configured to calibrate MS gates, and the calibration circuitincludes a first MS gate, a MS(θ) gate, and a second MS gate, an MS(−θ)gate, where θ represents an amount of entanglement of the respective MSgates.
 11. A quantum information processing (QIP) system for handlingasymmetric errors, comprising: an asymmetric error component configuredto control one or more components of the QIP system to: implement aquantum circuit in the QIP system, the quantum circuit having at least afirst qubit line and a second qubit line, wherein a first qubit state inthe QIP system has a greater measurement error than a second qubit statein the QIP system; swap a first representation of the first qubit stateand a second representation of the second qubit state at a quantumcircuit level in response to at least one of the first qubit line andthe second qubit line being expected to be at the first qubit state atmeasurement; and enable a quantum simulation using the quantum circuitwith the first qubit state and the second qubit state reassigned in atleast one of the first qubit line and the second qubit line after theswapping of the respective representations.
 12. The QIP system of claim11, wherein the one or more components of the QIP system include one ormore of a trap, an optical controller, an algorithms component, or oneor more sub-components of the trap, the optical controller or thealgorithms component.
 13. The QIP system of claim 11, wherein thequantum circuit is part of a quantum chemistry circuit and the quantumsimulation is a quantum chemistry simulation, and wherein the asymmetricerror component is configured to control one or more components toperform the quantum chemistry simulation using the quantum chemistrycircuit with the reassigned first qubit state and second qubit state forthe first qubit line and/or the second qubit line.
 14. The QIP system ofclaim 13, wherein, prior to the reassigning of the first qubit state andthe second qubit state, the first qubit state indicates that an electronis in an orbital and the second qubit state indicates that there is noelectron in an orbital, and wherein the first qubit line corresponds toa top orbital and the second qubit line corresponds to a bottom orbital.15. The QIP system of claim 14, wherein, after the reassigning of thefirst qubit state and the second qubit state, the first qubit stateindicates that there is no electron in an orbital and the second qubitstate indicates that there is an electron in an orbital.
 16. The QIPsystem of claim 11, wherein the asymmetric error component is configuredto control one or more components to implement the quantum circuit byapplying a NOT gate to a start of the first qubit line to implement thereassigning of the first qubit state and the second qubit state orapplying the representations of the first qubit state and the secondqubit state in the quantum circuit.
 17. The QIP system of claim 16,wherein the asymmetric error component is configured to control one ormore components to applying the NOT gate by propagating the NOT gatefrom the start of the first qubit line to an end of the first qubit lineto preserve an equivalence.
 18. The QIP system of claim 16, wherein theasymmetric error component is configured to control one or morecomponents to propagate the NOT gate to the end of the first qubit linebased one or more rules in connection with one or more gates in thequantum circuit, the one or more rules including: the NOT gate followedby an Rz(Ø) gate is equivalent to an Rz(−Ø) gate followed by the NOTgate (NOT-Rz(Ø)=Rz(−Ø)-NOT), the NOT gate followed by a Mølmer-Sørensen(MS) gate, MS(θ) gate, is equivalent to an MS(θ) gate followed by theNOT gate (NOT-MS(θ)=MS(θ)-NOT), where MS(θ) gate is acontinuous-parameter MS gate and θ is a degree or amount of entanglementof the MS gate, or the NOT gate followed by a Hadamard gate, H gate, isequivalent to an H gate followed by a Z gate (NOT-H=H−Z).
 19. The QIPsystem of claim 18, wherein the asymmetric error component is configuredto: control one or more components to propagate the NOT gate to the endof the first qubit line based on the one or more rules results in eithera NOT gate or a Z gate at the end of the first qubit line; and inresponse to the first qubit line ending in the NOT gate and then ameasurement being made, perform the measurement and a classical flip,or, in response to the first qubit line ending in the Z gate and then ameasurement being made, perform the measurement.
 20. The QIP system ofclaim 11, wherein: the quantum circuit is a calibration circuitconfigured to calibrate MS gates, and the calibration circuit includes afirst MS gate, a MS(θ) gate, and a second MS gate, an MS(−θ) gate, whereθ represents an amount of entanglement of the respective MS gates.